In a large bowl, using a rubber spatula, mix the butter, blue cheese, bacon, and chives together until combined. Dollop half of the compound butter along the long edge of a 12-inch piece of parchment or waxed paper. Roll into a log, twisting opposite ways on both ends of the paper to create a tightly wrapped log of butter. Refrigerate or freeze for another use.
Preheat the oven to 425 degrees F.
Using your fingers, carefully loosen the skin from chicken breasts. Stuff about 1/4 of the remaining blue cheese butter under the skin of each breast; smoothing the skin to evenly distribute the butter over the surface of the breast meat.
Put the chicken on a rimmed baking sheet and rub any remaining butter over the skin. Season each breast with just a pinch of freshly ground black pepper.
Roast the chicken breasts, skin sides up, in the center of the oven until skin is crisped and chicken is cooked through, about 35 to 40 minutes. An instant-read thermometer should register 165 degrees F when inserted into the thickest part of the meat. Remove from the oven to a serving platter. Let stand 10 minutes before serving.
Cook's Note: This recipe makes 2 logs of compound butter; unused butter can be used to top grilled meats, burgers, or baked or mashed potatoes.